For various applications it is useful to determine the relative localization of a number of sensors. In the case of sensors, this allows the determination of spatial information about the sensed signal. Useful information can also be obtained from determining the location of a set of microphones. For example, such information can be used to determine the location of sound sources producing the audio being captured by the microphones. The information can also be used to separate sound signals produced by different sounds sources, such as talking persons or musical instruments. In such a scenario, knowledge of the location of the microphones facilitates the usage of physical models, likely providing an advantage over separation methods that do not require the scenario to be physically plausible.
For example, imagine a set of microphones (e.g., mobile telephones or Smartphones) are in a room. The basic problem is to compute their location from their observation of a set of acoustic events. A number of solutions to these basic problems have been proposed. However, these proposed solutions either do not consider unknown internal delays at the microphone (referred to herein as “observation delays”), or they suffer from local minima far away from the true solution.